3 * Textual representation of multiprecision numbers
5 * (c) 1999 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
12 * Catacomb is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU Library General Public License as
14 * published by the Free Software Foundation; either version 2 of the
15 * License, or (at your option) any later version.
17 * Catacomb is distributed in the hope that it will be useful,
18 * but WITHOUT ANY WARRANTY; without even the implied warranty of
19 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
20 * GNU Library General Public License for more details.
22 * You should have received a copy of the GNU Library General Public
23 * License along with Catacomb; if not, write to the Free
24 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
28 /*----- Header files ------------------------------------------------------*/
34 #include <mLib/macros.h>
40 /*----- Magical numbers ---------------------------------------------------*/
42 /* --- Maximum recursion depth --- *
44 * This is the number of bits in a @size_t@ object. Why?
46 * To see this, let %$b = \textit{MPW\_MAX} + 1$% and let %$Z$% be the
47 * largest @size_t@ value. Then the largest possible @mp@ is %$M - 1$% where
48 * %$M = b^Z$%. Let %$r$% be a radix to read or write. Since the recursion
49 * squares the radix at each step, the highest number reached by the
50 * recursion is %$d$%, where:
54 * Solving gives that %$d = \lg \log_r b^Z$%. If %$r = 2$%, this is maximum,
55 * so choosing %$d = \lg \lg b^Z = \lg (Z \lg b) = \lg Z + \lg \lg b$%.
57 * Expressing %$\lg Z$% as @CHAR_BIT * sizeof(size_t)@ yields an
58 * overestimate, since a @size_t@ representation may contain `holes'.
59 * Choosing to represent %$\lg \lg b$% by 10 is almost certainly sufficient
60 * for `some time to come'.
63 #define DEPTH (CHAR_BIT * sizeof(size_t) + 10)
65 /*----- Input -------------------------------------------------------------*/
67 /* --- @mp_read@ --- *
69 * Arguments: @mp *m@ = destination multiprecision number
70 * @int radix@ = base to assume for data (or zero to guess)
71 * @const mptext_ops *ops@ = pointer to operations block
72 * @void *p@ = data for the operations block
74 * Returns: The integer read, or zero if it didn't work.
76 * Use: Reads an integer from some source. If the @radix@ is
77 * specified, the number is assumed to be given in that radix,
78 * with the letters `a' (either upper- or lower-case) upwards
79 * standing for digits greater than 9. Otherwise, base 10 is
80 * assumed unless the number starts with `0' (octal), `0x' (hex)
81 * or `nnn_' (base `nnn'). An arbitrary amount of whitespace
82 * before the number is ignored.
85 /* --- About the algorithm --- *
87 * The algorithm here is rather aggressive. I maintain an array of
88 * successive squarings of the radix, and a stack of partial results, each
89 * with a counter attached indicating which radix square to multiply by.
90 * Once the item at the top of the stack reaches the same counter level as
91 * the next item down, they are combined together and the result is given a
92 * counter level one higher than either of the results.
94 * Gluing the results together at the end is slightly tricky. Pay attention
97 * This is more complicated because of the need to handle the slightly
101 static int char_digit(int ch, int radix)
103 int r = radix < 0 ? -radix : radix;
106 if (ch < 0) return (-1);
107 if (radix < 0) d = ch;
108 else if ('0' <= ch && ch <= '9') d = ch - '0';
109 else if ('a' <= ch && ch <= 'z') d = ch - 'a' + 10;
110 else if ('A' <= ch && ch <= 'Z') d = ch - 'A' + (radix > 36 ? 36 : 10);
112 if (d >= r) return (-1);
116 static mp *read_binary(int radix, unsigned bit, unsigned nf,
117 const mptext_ops *ops, void *p)
120 unsigned b = MPW_BITS;
127 /* --- The fast binary algorithm --- *
129 * We stack bits up starting at the top end of a word. When one word is
130 * full, we write it to the integer, and start another with the left-over
131 * bits. When the array in the integer is full, we resize using low-level
132 * calls and copy the current data to the top end. Finally, we do a single
133 * bit-shift when we know where the end of the number is.
136 m = mp_dest(MP_NEW, 1, nf);
143 if ((d = char_digit(ch, radix)) < 0) break;
145 /* --- Ignore leading zeroes, but notice that the number is valid --- */
148 if (!d && !nz) continue;
151 /* --- Feed the digit into the accumulator --- */
157 a |= MPW(d) >> (bit - b);
162 v = mpalloc(m->a, len);
163 memcpy(v + n, m->v, MPWS(n));
165 m->v = v; v = m->v + n;
167 a = (b < MPW_BITS) ? MPW(d) << b : 0;
171 /* --- Finish up --- */
174 if (!any) { mp_drop(m); return (0); }
180 m = mp_lsr(m, m, (unsigned long)n * MPW_BITS + b);
187 /* --- State for the general-base reader --- *
189 * There are two arrays. The @pow@ array is set so that @pow[i]@ contains
190 * %$R^{2^i}$% for @i < pows@. The stack @s@ contains partial results:
191 * each entry contains a value @m@ corresponding to %$2^i$% digits.
192 * Inductively, an empty stack represents zero; if a stack represents %$x$%
193 * then pushing a new entry on the top causes the stack to represent
196 * It is an invariant that each entry has a strictly smaller @i@ than the
197 * items beneath it. This is achieved by coaslescing entries at the top if
198 * they have equal %$i$% values: if the top items are %$(m, i)$%, and
199 * %$(M', i)$%, and the rest of the stack represents the integer %$x$%,
200 * then %$R^{2^i} (R^{2^i} x + M) + m = R^{2^{i+1}} x + (R^{2^i} M + m)$%,
201 * so we replace the top two items by %$((R^{2^i} M + m), i + 1)$%, and
202 * repeat if necessary.
206 struct { unsigned i; mp *m; } s[DEPTH];
210 static void ensure_power(struct readstate *rs)
212 /* --- Make sure we have the necessary %$R^{2^i}$% computed --- */
214 if (rs->s[rs->sp].i >= rs->pows) {
215 assert(rs->pows < DEPTH);
216 rs->pow[rs->pows] = mp_sqr(MP_NEW, rs->pow[rs->pows - 1]);
221 static void read_digit(struct readstate *rs, unsigned nf, int d)
223 mp *m = mp_new(1, nf);
226 /* --- Put the new digit on top --- */
228 assert(rs->sp < DEPTH);
232 /* --- Restore the stack invariant --- */
234 while (rs->sp && rs->s[rs->sp - 1].i <= rs->s[rs->sp].i) {
240 m = mp_mul(m, m, rs->pow[rs->s[rs->sp + 1].i]);
241 m = mp_add(m, m, rs->s[rs->sp + 1].m);
242 MP_DROP(rs->s[rs->sp + 1].m);
247 /* --- Leave the stack pointer at an empty item --- */
252 static mp *read_general(int radix, unsigned t, unsigned nf,
253 const mptext_ops *ops, void *p)
264 /* --- Prepare the stack --- */
266 r = radix < 0 ? -radix : radix;
267 mp_build(&rr, &r, &r + 1);
272 /* --- If we've partially parsed some input then feed it in --- *
274 * Unfortunately, what we've got is backwards. Fortunately there's a
275 * fairly tight upper bound on how many digits @t@ might be, since we
276 * aborted that loop once it got too large.
281 while (t) { assert(i < sizeof(v)); v[i++] = t%r; t /= r; }
282 while (i) read_digit(&rs, nf, v[--i]);
286 /* --- Read more stuff --- */
290 if ((d = char_digit(ch, radix)) < 0) break;
291 read_digit(&rs, nf, d); any = 1;
295 /* --- Stitch all of the numbers together --- *
297 * This is not the same code as @read_digit@. In particular, here we must
298 * cope with the partial result being some inconvenient power of %$R$%,
299 * rather than %$R^{2^i}$%.
302 if (!any) return (0);
303 m = MP_ZERO; z = MP_ONE;
310 z = mp_mul(z, z, rs.pow[rs.s[rs.sp].i]);
313 for (i = 0; i < rs.pows; i++) MP_DROP(rs.pow[i]);
318 mp *mp_read(mp *m, int radix, const mptext_ops *ops, void *p)
328 /* --- We don't actually need a destination so throw it away --- *
330 * But note the flags before we lose it entirely.
338 /* --- Maintain a lookahead character --- */
342 /* --- If we're reading text, skip leading space, and maybe a sign --- */
345 while (ISSPACE(ch)) ch = ops->get(p);
347 case '-': f |= f_neg; /* and on */
348 case '+': do ch = ops->get(p); while (ISSPACE(ch));
352 /* --- If we don't have a fixed radix, then parse one from the input --- *
354 * This is moderately easy if the input starts with `0x' or similar. If it
355 * starts with `0' and something else, then it might be octal, or just a
356 * plain old zero. Finally, it might start with a leading `NN_', in which
357 * case we carefully collect the decimal number until we're sure it's
358 * either a radix prefix (in which case we accept it and start over) or it
359 * isn't (in which case it's actually the start of a large number we need
367 case 'x': case 'X': radix = 16; goto fetch;
368 case 'o': case 'O': radix = 8; goto fetch;
369 case 'b': case 'B': radix = 2; goto fetch;
370 fetch: ch = ops->get(p); break;
371 default: radix = 8; f |= f_ok; break;
374 if ((d = char_digit(ch, 10)) < 0) { ops->unget(ch, p); return (0); }
379 if ((d = char_digit(ch, 10)) < 0) break;
381 if (ch != '_' || t > 52) radix = 10;
389 /* --- We're now ready to dispatch to the correct handler --- */
391 rd = radix < 0 ? -radix : radix;
394 case 2: m = read_binary(radix, 1, nf, ops, p); break;
395 case 4: m = read_binary(radix, 2, nf, ops, p); break;
396 case 8: m = read_binary(radix, 3, nf, ops, p); break;
397 case 16: m = read_binary(radix, 4, nf, ops, p); break;
398 case 32: m = read_binary(radix, 5, nf, ops, p); break;
399 case 64: m = read_binary(radix, 6, nf, ops, p); break;
400 case 128: m = read_binary(radix, 7, nf, ops, p); break;
401 default: m = read_general(radix, t, nf, ops, p); break;
404 /* --- That didn't work --- *
406 * If we've already read something then return that. Otherwise it's an
411 if (f & f_ok) return (MP_ZERO);
415 /* --- Negate the result if we should do that --- */
417 if (f & f_neg) m = mp_neg(m, m);
419 /* --- And we're all done --- */
427 /*----- Output ------------------------------------------------------------*/
429 /* --- @mp_write@ --- *
431 * Arguments: @mp *m@ = pointer to a multi-precision integer
432 * @int radix@ = radix to use when writing the number out
433 * @const mptext_ops *ops@ = pointer to an operations block
434 * @void *p@ = data for the operations block
436 * Returns: Zero if it worked, nonzero otherwise.
438 * Use: Writes a large integer in textual form.
441 static int digit_char(int d, int radix)
443 if (radix < 0) return (d);
444 else if (d < 10) return (d + '0');
445 else if (d < 26) return (d - 10 + 'a');
446 else return (d - 36 + 'A');
449 /* --- Simple case --- *
451 * Use a fixed-sized buffer and single-precision arithmetic to pick off
452 * low-order digits. Put each digit in a buffer, working backwards from the
453 * end. If the buffer becomes full, recurse to get another one. Ensure that
454 * there are at least @z@ digits by writing leading zeroes if there aren't
455 * enough real digits.
458 static int write_simple(mpw n, int radix, unsigned z,
459 const mptext_ops *ops, void *p)
463 unsigned i = sizeof(buf);
464 int rd = radix > 0 ? radix : -radix;
469 buf[--i] = digit_char(x, radix);
474 rc = write_simple(n, radix, z, ops, p);
477 memset(zbuf, (radix < 0) ? 0 : '0', sizeof(zbuf));
478 while (!rc && z >= sizeof(zbuf)) {
479 rc = ops->put(zbuf, sizeof(zbuf), p);
482 if (!rc && z) rc = ops->put(zbuf, z, p);
484 if (!rc) rc = ops->put(buf + i, sizeof(buf) - i, p);
489 /* --- Complicated case --- *
491 * If the number is small, fall back to the simple case above. Otherwise
492 * divide and take remainder by current large power of the radix, and emit
493 * each separately. Don't emit a zero quotient. Be very careful about
494 * leading zeroes on the remainder part, because they're deeply significant.
497 static int write_complicated(mp *m, int radix, mp **pr,
498 unsigned i, unsigned z,
499 const mptext_ops *ops, void *p)
506 return (write_simple(MP_LEN(m) ? m->v[0] : 0, radix, z, ops, p));
509 mp_div(&q, &m, m, pr[i]);
510 if (MP_ZEROP(q)) d = z;
514 rc = write_complicated(q, radix, pr, i - 1, z, ops, p);
516 if (!rc) rc = write_complicated(m, radix, pr, i - 1, d, ops, p);
521 /* --- Binary case --- *
523 * Special case for binary output. Goes much faster.
526 static int write_binary(mp *m, int bit, int radix,
527 const mptext_ops *ops, void *p)
541 /* --- Work out where to start --- */
544 if (n % bit) n += bit - (n % bit);
548 if (n >= MP_LEN(m)) {
555 mask = (1 << bit) - 1;
558 /* --- Main code --- */
567 if (v == m->v) break;
569 if (b < MPW_BITS) x |= a >> b;
572 if (!x && !(f & f_out)) continue;
574 *q++ = digit_char(x, radix);
575 if (q >= buf + sizeof(buf)) {
576 if ((rc = ops->put(buf, sizeof(buf), p)) != 0) goto done;
583 *q++ = digit_char(x, radix);
584 rc = ops->put(buf, q - buf, p);
593 /* --- Main driver code --- */
595 int mp_write(mp *m, int radix, const mptext_ops *ops, void *p)
603 if (MP_EQ(m, MP_ZERO))
604 return (ops->put(radix > 0 ? "0" : "\0", 1, p));
606 /* --- Set various things up --- */
611 /* --- Check the radix for sensibleness --- */
614 assert(((void)"ascii radix must be <= 62", radix <= 62));
616 assert(((void)"binary radix must fit in a byte", -radix <= UCHAR_MAX));
618 assert(((void)"radix can't be zero in mp_write", 0));
620 /* --- If the number is negative, sort that out --- */
624 if (ops->put("-", 1, p)) return (EOF);
628 /* --- Handle binary radix --- */
631 case 2: case -2: return (write_binary(m, 1, radix, ops, p));
632 case 4: case -4: return (write_binary(m, 2, radix, ops, p));
633 case 8: case -8: return (write_binary(m, 3, radix, ops, p));
634 case 16: case -16: return (write_binary(m, 4, radix, ops, p));
635 case 32: case -32: return (write_binary(m, 5, radix, ops, p));
636 case -64: return (write_binary(m, 6, radix, ops, p));
637 case -128: return (write_binary(m, 7, radix, ops, p));
640 /* --- If the number is small, do it the easy way --- */
643 rc = write_simple(MP_LEN(m) ? m->v[0] : 0, radix, 0, ops, p);
645 /* --- Use a clever algorithm --- *
647 * Square the radix repeatedly, remembering old results, until I get
648 * something more than half the size of the number @m@. Use this to divide
649 * the number: the quotient and remainder will be approximately the same
650 * size, and I'll have split them on a digit boundary, so I can just emit
651 * the quotient and remainder recursively, in order.
655 target = (MP_LEN(m) + 1) / 2;
658 /* --- Set up the exponent table --- */
660 z->v[0] = (radix > 0 ? radix : -radix);
663 assert(((void)"Number is too unimaginably huge", i < DEPTH));
665 if (MP_LEN(z) > target) break;
666 z = mp_sqr(MP_NEW, z);
669 /* --- Write out the answer --- */
671 rc = write_complicated(m, radix, pr, i - 1, 0, ops, p);
673 /* --- Tidy away the array --- */
675 while (i > 0) mp_drop(pr[--i]);
678 /* --- Tidying up code --- */
684 /*----- Test rig ----------------------------------------------------------*/
688 #include <mLib/testrig.h>
690 static int verify(dstr *v)
693 int ib = *(int *)v[0].buf, ob = *(int *)v[2].buf;
696 mp *m = mp_readdstr(MP_NEW, &v[1], &off, ib);
699 fprintf(stderr, "*** unexpected successful parse\n"
700 "*** input [%2i] = ", ib);
702 type_hex.dump(&v[1], stderr);
704 fputs(v[1].buf, stderr);
705 mp_writedstr(m, &d, 10);
706 fprintf(stderr, "\n*** (value = %s)\n", d.buf);
709 mp_writedstr(m, &d, ob);
710 if (d.len != v[3].len || MEMCMP(d.buf, !=, v[3].buf, d.len)) {
711 fprintf(stderr, "*** failed read or write\n"
712 "*** input [%2i] = ", ib);
714 type_hex.dump(&v[1], stderr);
716 fputs(v[1].buf, stderr);
717 fprintf(stderr, "\n*** output [%2i] = ", ob);
719 type_hex.dump(&d, stderr);
721 fputs(d.buf, stderr);
722 fprintf(stderr, "\n*** expected [%2i] = ", ob);
724 type_hex.dump(&v[3], stderr);
726 fputs(v[3].buf, stderr);
734 fprintf(stderr, "*** unexpected parse failure\n"
735 "*** input [%2i] = ", ib);
737 type_hex.dump(&v[1], stderr);
739 fputs(v[1].buf, stderr);
740 fprintf(stderr, "\n*** expected [%2i] = ", ob);
742 type_hex.dump(&v[3], stderr);
744 fputs(v[3].buf, stderr);
750 if (v[1].len - off != v[4].len ||
751 MEMCMP(v[1].buf + off, !=, v[4].buf, v[4].len)) {
752 fprintf(stderr, "*** leftovers incorrect\n"
753 "*** input [%2i] = ", ib);
755 type_hex.dump(&v[1], stderr);
757 fputs(v[1].buf, stderr);
758 fprintf(stderr, "\n*** expected `%s'\n"
760 v[4].buf, v[1].buf + off);
765 assert(mparena_count(MPARENA_GLOBAL) == 0);
769 static test_chunk tests[] = {
770 { "mptext-ascii", verify,
771 { &type_int, &type_string, &type_int, &type_string, &type_string, 0 } },
772 { "mptext-bin-in", verify,
773 { &type_int, &type_hex, &type_int, &type_string, &type_string, 0 } },
774 { "mptext-bin-out", verify,
775 { &type_int, &type_string, &type_int, &type_hex, &type_string, 0 } },
779 int main(int argc, char *argv[])
782 test_run(argc, argv, tests, SRCDIR "/t/mptext");
788 /*----- That's all, folks -------------------------------------------------*/